Sharice Davids, the Democratic candidate, has a modest lead in our poll.

Our poll is a good result for Democrats. But remember: It’s just one poll, and we talked to only 494 people. Each candidate’s total could easily be five points different if we polled everyone in the district. And having a small sample is only one possible source of error.

About the race

Kevin Yoder is the current representative, first elected in 2010. 40% favorable rating; 49% unfavorable; 10% don’t know

Based on 494 interviews

This district, which includes western suburbs of Kansas City, Mo., went narrowly for Hillary Clinton in 2016, but a Republican incumbent has held the seat since 2011.

Mr. Yoder, who has been endorsed by President Trump, has found himself caught in the middle on certain issues, among them immigration. But he supported the tax overhaul bill and the effort to repeal Obamacare.

Ms. Davids, a Native American proficient in mixed martial arts, prevailed in a crowded primary field. She is among a wave of L.G.B.T. candidates pursuing a strategy that treats sexuality, race and gender as campaign assets as they warn about lost progress on civil rights and advance policy ideas.

Mr. Yoder grew up on a farm near Yoder, Kan. He is far ahead in fund-raising, with about $2.7 million versus $345,000 in the most recent report.

How our poll result changed

As we reach more people, our poll will become more stable and the margin of sampling error will shrink. The changes in the timeline below reflect that sampling error, not real changes in the race.

One reason we’re doing these surveys live is so you can see the uncertainty for yourself.

But sampling error is not the only type of error in a poll.

Our turnout model

There’s a big question on top of the standard margin of error in a poll: Who is going to vote? It’s a particularly challenging question this year, since special elections have shown Democrats voting in large numbers.

To estimate the likely electorate, we combine what people say about how likely they are to vote with information about how often they have voted in the past. In previous races, this approach has been more accurate than simply taking people at their word. But there are many other ways to do it.

Our poll under different turnout scenarios

Who will vote?

Est. turnout

Our poll result

The types of people who voted in 2014

227k

Davids +1

People who say they are almost certain to vote, and no one else

239k

Davids +14

Our estimate

266k

Davids +8

People whose voting history suggests they will vote, regardless of what they say

269k

Davids +6

People who say they will vote, adjusted for past levels of truthfulness

284k

Davids +7

The types of people who voted in 2016

324k

Davids +4

Every active registered voter

444k

Davids +1

All estimates based on 494 interviews

Just because one candidate leads in all of these different turnout scenarios doesn’t mean much by itself. They don’t represent the full range of possible turnout scenarios, let alone the full range of possible election results.

The types of people we reached

Even if we got turnout exactly right, the margin of error wouldn’t capture all of the error in a poll. The simplest version assumes we have a perfect random sample of the voting population. We do not.

People who respond to surveys are almost always too old, too white, too educated and too politically engaged to accurately represent everyone.

How successful we were in reaching different kinds of voters

Called

Inter-viewed

Successrate

Ourrespon­ses

Goal

18 to 29

1788

52

1 in 34

11%

9%

30 to 64

11909

292

1 in 41

59%

62%

65 and older

4143

150

1 in 28

30%

29%

Male

7440

232

1 in 32

47%

47%

Female

10402

262

1 in 40

53%

53%

White

14297

401

1 in 36

81%

79%

Nonwhite

1885

48

1 in 39

10%

11%

Cell

13477

387

1 in 35

78%

—

Landline

4365

107

1 in 41

22%

—

Based on administrative records. Some characteristics are missing or incorrect. Many voters are called multiple times.

Pollsters compensate by giving more weight to respondents from under-represented groups.

But weighting works only if you weight by the right categories and you know what the composition of the electorate will be. In 2016, many pollsters didn’t weight by education and overestimated Hillary Clinton’s standing as a result.

Here are other common ways to weight a poll:

Our poll under different weighting schemes

Our poll result

Don’t weight by education, like many polls in 2016

Davids +9

Don’t weight by party registration, like most public polls

Davids +8

Our estimate

Davids +8

Weight using census data instead of voting records, like most public polls

Davids +8

All estimates based on 494 interviews

Just because one candidate leads in all of these different weighting scenarios doesn’t mean much by itself. They don’t represent the full range of possible weighting scenarios, let alone the full range of possible election results.

Undecided voters

About 6 percent of voters said that they were undecided or refused to tell us whom they would vote for. On questions about issues, these voters most closely resembled Democrats.

They are not numerous enough to change the lead in our poll by themselves. But they — and others — could change their minds. (We could also be wrong on turnout or our sample could be unrepresentative.)

Issues and other questions

We're asking voters whether they support the North American Free Trade Agreement (Nafta), President Trump's tariffs on steel and aluminum, and the tax bill. And we’re asking if they feel the president’s policies have improved their economic situation.

We’re also asking voters whether they support Brett Kavanaugh’s nomination to the United States Supreme Court.

Do you approve or disapprove of the job Donald Trump is doing as president?

Approve

Disapp.

Don’t know

Voters n = 494

41%

56%

3%

Would you prefer Republicans to retain control of the House of Representatives or would you prefer Democrats to take control?

Reps. keep House

Dems. take House

Don’t know

Voters n = 494

43%

51%

6%

Do you support or oppose the North American Free Trade Agreement between the U.S., Canada and Mexico?

Support

Oppose

Don’t know

Voters n = 494

60%

27%

13%

Do you support or oppose the tariffs on steel and aluminum imposed by President Trump this year?

Support

Oppose

Don’t know

Voters n = 494

34%

56%

10%

Do you support or oppose the tax reform bill passed by Congress and signed by the president last year?

Support

Oppose

Don’t know

Voters n = 494

48%

46%

6%

Do you agree or disagree that President Trump’s policies have made you and your family’s economic situation better?

agree

disagree

Don’t know

Voters n = 494

48%

48%

4%

Do you support or oppose Brett Kavanaugh’s nomination to the United States Supreme Court?

support

oppose

Don’t know

Voters n = 494

42%

48%

9%

Percentages are weighted to resemble likely voters.

What different types of voters said

Voters nationwide are deeply divided along demographic lines. Our poll suggests divisions too. But don’t overinterpret these tables. Results among subgroups may not be representative or reliable. Be especially careful with groups with fewer than 100 respondents, shown here in stripes.

Gender

Dem.

Rep.

Und.

Female n = 262 / 53% of voters

58%

36%

6%

Male 232 / 47%

43%

52%

6%

Age

Dem.

Rep.

Und.

18 to 29 n = 53 / 11% of voters

62%

35%

4%

30 to 44 109 / 22%

64%

32%

4%

45 to 64 180 / 39%

41%

51%

7%

65 and older 152 / 29%

49%

44%

7%

Race

Dem.

Rep.

Und.

White n = 421 / 84% of voters

50%

45%

5%

Nonwhite 65 / 14%

59%

29%

12%

Race and education

Dem.

Rep.

Und.

Nonwhite n = 65 / 14% of voters

59%

29%

12%

White, college grad 273 / 54%

54%

42%

4%

White, not college grad 148 / 30%

43%

50%

7%

Education

Dem.

Rep.

Und.

H.S. Grad. or Less n = 32 / 13% of voters

30%

50%

19%

Some College Educ. 149 / 25%

53%

45%

3%

4-year College Grad. 170 / 38%

54%

43%

4%

Post-grad. 141 / 23%

56%

38%

6%

Party

Dem.

Rep.

Und.

Democrat n = 145 / 30% of voters

92%

5%

3%

Republican 171 / 34%

11%

88%

2%

Independent 166 / 34%

57%

32%

12%

Another party 7 / 1%

24%

76%

—

Party registration

Dem.

Rep.

Und.

Democratic n = 155 / 31% of voters

85%

9%

6%

Republican 226 / 46%

23%

72%

5%

Other 113 / 23%

59%

34%

7%

Intention of voting

Dem.

Rep.

Und.

Almost certain n = 320 / 67% of voters

55%

42%

3%

Very likely 127 / 25%

49%

45%

6%

Somewhat likely 28 / 6%

27%

51%

22%

Not very likely 12 / 2%

23%

40%

37%

Not at all likely 6 / 1%

45%

35%

21%

Percentages are weighted to resemble likely voters; the number of respondents in each subgroup is unweighted. Undecided voters includes those who refused to answer.

This survey was conducted by The New York Times Upshot and Siena College.

Data collection by Reconnaissance Market Research, M. Davis and Company, the Institute for Policy and Opinion Research at Roanoke College, the Survey Research Center at the University of Waterloo, the University of North Florida and the Siena College Research Institute.